**Introduction to Topology (TOP1)**

*Instructor:* Dr. Ágnes Szilard

*Text:* Class notes, and notes distributed in class.

*Reference book:*
Munkres: Topology, Prentice Hall, 2000

*Prerequisites*: Calculus, basics of set theory and group
theory.

*Course description*: This is a standard introductory course
the goal of which is to get acquainted with the basic notions of the field.
Thus we start with point-set topology and a thorough discussion of metric and
topological spaces, continuity, connectedness, compactness.
We then get a glimpse of algebraic topology - the notion of the
fundamental group of a topological space will be introduced and we will
study covering spaces. The machinery developed will allow us to
look at one of the major theorems of topology:
the classification of compact surfaces.

Throughout the course we will study numerous examples and applications.